Lunar Ascent Research Articles

Multi-disciplinary optimization of single-stage hybrid rockets for lunar ascent

This study aims to determine the optimal design and ascent trajectory for a single-stage hybrid rocket in the context of a lunar ascent mission, with the objective of reaching a 100 km circular orbit on the Moon equatorial plane. A multi-disciplinary optimization problem is formulated, integrating flight design variables and launch vehicle design variables to achieve the best mission scenario. A zero-dimensional internal ballistics model is employed to estimate key parameters such as thrust, mass flow rate, and gross mass of the hybrid rocket, while a three-degree of freedom dynamical model is utilized to simulate the ascent trajectory. The resulting integrated optimization problem is solved using an in-house heuristic algorithm that combines particle swarm and genetic algorithms. Two propellant combinations, liquid oxygen/paraffin-wax and hydrogen peroxide (90%)/high-density polyethylene, are evaluated, considering both their performance in the integrated system and the feasibility of the proposed mission. After conducting a sensitivity analysis to investigate the influence of particle count in the optimization process, results for both propellant combinations are presented. While paraffin and oxygen provide the highest payload ratio, hydrogen peroxide and polyethylene entail a more feasible and flexible design for a lunar mission.

Design and implementation of GNC system of lander and ascender module of Chang’e-5 spacecraft

<p indent="0mm">The lander and ascender module of Chang’e-5 spacecraft achieved China’s first lunar landing and ascent mission. The guidance, navigation, and control (GNC) system is one of the most important subsystems. To meet the weight, safety, and intelligence requirement of the mission, light-weight integration designs are implemented in the GNC system, so that a single control system could meet the mission requirement of landing, ascent, and rendezvous. Moreover, a high-rate robust optical obstacle avoidance system is applied with a hierarchical controller, and landing security is enhanced while fuel consumption is minimized. Furthermore, autonomous attitude determination on the lunar surface and orbit insertion are achieved during the lunar ascent phase, and momentum wheels are relied on to obtain good attitude stability for the spacecraft during the rendezvous phase. Finally, the GNC system has fully functional redundancy and autonomous management, which significantly increases the fault detection and isolation capabilities. Here, we present key design specifications and implementations in the GNC system of the lander and ascender module.

Neighboring optimal guidance and constrained attitude control applied to three-dimensional lunar ascent and orbit injection

Future human or robotic missions to the Moon will require efficient ascent path and accurate orbit injection maneuvers, because the dynamical conditions at injection affect the subsequent phases of spaceflight. This research is focused on the original combination of two techniques applied to lunar ascent modules, i.e. (i) the recently-introduced variable-time-domain neighboring optimal guidance (VTD-NOG), and (ii) a constrained proportional-derivative (CPD) attitude control algorithm. VTD-NOG belongs to the class of implicit guidance approaches, aimed at finding the corrective control actions capable of maintaining the spacecraft sufficiently close to the reference trajectory. CPD pursues the desired attitude using thrust vector control and side jet system, while constraining the rates of both the thrust deflection angle and the roll control torque. After determining the optimal two-dimensional ascent path, which represents the reference trajectory, VTD-NOG & CPD is applied in the presence of nonnominal flight conditions, namely those due to navigation and actuation errors, incorrect initial position, unpredictable oscillations of the propulsive thrust, and imperfect modeling of the spacecraft mass distribution and variation. These stochastic deviations are simulated in the context of extensive Monte Carlo campaigns, and yield three-dimensional perturbed trajectories. The numerical results obtained in this work unequivocally demonstrate that VTD-NOG & CPD represents an accurate and effective methodology for guidance and control of lunar ascent path and orbit injection.

Lunar Ascent and Orbit Injection via Neighboring Optimal Guidance and Constrained Attitude Control

AbstractFuture human or robotic missions to the Moon will require efficient ascent path and accurate orbit injection maneuvers, because the dynamical conditions at injection affect the subsequent p...

Optimal Mirror Trajectories Using Continuous Thrust

The theorem of mirror trajectories, proven almost six decades ago by Miele, states that for a given path in the restricted problem of three bodies (with primaries in mutual circular orbits) there exists a mirror trajectory (in two dimensions) and three mirror paths (in three dimensions). The theorem at hand regards feasible trajectories and proved extremely useful for investigating the spacecraft natural dynamics in the circular restricted problem of three bodies, by identifying special solutions, such as symmetric periodic orbits and free return paths. This theorem has recently been extended to optimal mirror trajectories, thus substantiating Miele's conjecture based on numerical evidence. Unlike the theorem of mirror paths, which refers to natural (unpowered) orbital motion, the theorem of optimal mirror trajectories establishes the existence, characteristics, and optimal control time history of the returning path, once the outgoing optimal trajectory has been determined. This theorem applies to (i) nite-thrust trajectories, for which a limiting value of the thrust acceleration exists, (ii) constant-thrust-acceleration paths, (iii) impulsive trajectories, and (iv) articial periodic orbits (that use very low thrust propulsion or solar sails). This work illustrates the theorem of optimal mirror trajectories applied to two cases of practical interest: (a) continuous, low-thrust orbit transfer, and (b) continuous-thrust lunar descent (with soft touchdown) and ascent (with nal orbit injection). In both cases, the theorem allows the immediate and straightforward identication of the optimal control law of the returning path, once the outgoing optimal trajectory has been determined.

A unified trajectory optimization framework for lunar ascent

This paper presents a unified trajectory optimization framework for lunar ascent. Compared with prevailing and emerging studies on lunar ascent trajectory optimization with simplified lunar ascent process and simple constraints, our method formulates in detail the lunar ascent process with complex constraints in a unified manner. The kinematics and dynamics model of lunar ascent with mission-specific constraints explicitly expressed through equalities or inequalities form the fuel-optimal lunar ascent trajectory optimization problem. A proper direct trajectory optimization method is chosen to transcribe the original trajectory optimization problem into a nonlinear programming (NLP) problem solved by a highly efficient NLP solver. The homotopy-based backtracking initial value strategy is designed to enhance convergence of the solving process. First, a two-phase trajectory optimization problem including vertical-rise phase and orbit-insertion phase is solved in the proposed unified framework. Subsequently, to obtain terrain clearance, we directly incorporate terrain description into the lunar ascent problem to obtain the optimal lunar ascent trajectory. Simulation results indicate that the proposed unified trajectory optimization framework has enough adaptability to efficiently handle complex lunar ascent scenarios. The proposed framework may benefit future autonomous lunar ascent missions.

Variable-time-domain neighboring optimal guidance applied to space trajectories

This research describes and applies the recently introduced, general-purpose variable-time-domain neighboring optimal guidance scheme, which is capable of driving a space vehicle in the proximity of a specified nominal, optimal path. This goal is achieved by minimizing the second differential of the objective function (related to fuel consumption) along the perturbed trajectory. This minimization principle leads to deriving all the corrective maneuvers, in the context of a closed-loop guidance scheme. Several time-varying gain matrices, referring to the nominal trajectory, are defined, computed offline, and stored in the onboard computer. Original analytical developments, based on optimal control theory and adoption of a variable time domain, constitute the theoretical foundation for three relevant features that characterize the guidance algorithm used in this work: (i) a new, efficient law for the real-time update of the time of flight (usually referred to as time-to-go), (ii) a new, effective termination criterion, and (iii) a new formulation of the sweep method. As a first application, this paper considers minimum-time lunar ascent and descent paths, under the flat Moon approximation. The second application is represented by the minimum-time, continuous-thrust orbit transfer between two coplanar circular orbits. In both cases, the nominal trajectories are two-dimensional, while the corresponding perturbed paths are three-dimensional. Specifically, perturbations arising from the imperfect knowledge of the propulsive parameters and from errors in the initial conditions are included in the dynamical simulations. Extensive Monte Carlo tests are performed, and definitely prove the effectiveness and accuracy of the variable-time-domain neighboring optimal guidance algorithm.

One Step Back, One Giant Leap Forward

This paper describes the vision for Space Exploration that would return humans to the moon by 2020. Creating architecture for returning humans to the moon requires the comprehension of the physics of spaceflight, knowledge of the hardware that can realize the physics, and an understanding of how these many parts interact and interconnect. The NASA team concluded early in its study that the direct–direct mode would be possible only if a single launch vehicle approaching twice the lift capacity of the Saturn V were available. The three mission modes were compared as higher levels of technology were engaged. The key was to find a workable architecture that involved the least amount of mass. The direct return mission that involved no operations in lunar orbit seems to be the least operationally complex, but it tends to be the least efficient because it moves the largest mass-including the Earth-entry heat shield- the entire velocity change of lunar landing and ascent.